Solve 10/sqrt{3^2+4sqrt{5}}

$$\frac { 10 } { \sqrt { 3 ^ { 2 } + 4 } \sqrt { 5 } }$$

Evaluate

$$\frac{2\sqrt{65}}{13}\approx 1.240347346$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\frac{10}{\sqrt{9+4}\sqrt{5}}$$

Add 9 and 4 to get 13.

$$\frac{10}{\sqrt{13}\sqrt{5}}$$

To multiply \sqrt{13} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{10}{\sqrt{65}}$$

Rationalize the denominator of \frac{10}{\sqrt{65}} by multiplying numerator and denominator by \sqrt{65}.

$$\frac{10\sqrt{65}}{\left(\sqrt{65}\right)^{2}}$$

The square of \sqrt{65} is 65.

$$\frac{10\sqrt{65}}{65}$$

Divide 10\sqrt{65} by 65 to get \frac{2}{13}\sqrt{65}.

$$\frac{2}{13}\sqrt{65}$$